Sir Michael Scholar said the PM used data that was "not comparable" in a podcast last week.

The podcast prompted complaints from opposition politicians, who accused Mr Brown of misleading the public on migrant numbers.

In a letter published today, Sir Michael pointed to two errors in the Downing Street internet broadcast.

Mr Brown claimed net inward migration – the number of arrivals minus those leaving – had fallen from 237,000 in 2007 to 163,000 in 2008 and 147,000 last year.

But Sir Michael said the correct figure for 2007 was 233,000. More seriously, he said the 147,000 figure used by Mr Brown was wrong because it was taken from a different data set which has not yet been adjusted.

It was taken from the International Passenger Survey, while the figures Mr Brown used for 2007 and 2008 were Long Term International Migration figures.

In previous years the final LTIM number has been up to 34,000 higher than the IPS data.

Sir Michael wrote that he hoped the political parties would be "careful" in their use of statistics in coming weeks.

He wrote: "I have received representations from several sources about your recent podcast on migration.

"I attach a note, prepared by the ONS, on these statistics. You will see that the note points out that the podcast did not use comparable data series for 2007 to 2009, and that it did not take account of the revised estimate of long-term net immigration for 2007.

"I note that in your speech today you correctly referred to the statistics in respect of migration for the period 2007 to 2009.

"The Statistics Authority hopes that, in the political debate over the coming weeks, all parties will be careful in their use of statistics, to protect the integrity of official statistics."

Shadow home secretary Chris Grayling said: "Gordon Brown is turning into a serial offender in misleading the British people in the run-up to the election.

"He gave false information to the Chilcot inquiry, his advertising campaign about policing was banned, and now he has given an inaccurate picture of his record on immigration. Britain should expect better from its Prime Minister. No wonder we need change."